SECTION 4: TRANSMISSION LINES. ESE 470 Energy Distribution Systems

Size: px
Start display at page:

Download "SECTION 4: TRANSMISSION LINES. ESE 470 Energy Distribution Systems"

Transcription

1 SECTION 4: TRANSMISSION LINES ESE 470 Energy Distribution Systems

2 2 Introduction

3 Transmission Lines 3 Transmission and distribution of electrical power occurs over metal cables Overhead AC or DC Underground AC or DC In the U.S. nearly all transmission makes use of overhead AC lines These cables are good, but not perfect, conductors Series impedance Shunt admittance In this section of notes we ll look at how these are accounted for in equivalent circuit models

4 Electrical Properties of Transmission Lines 4 Series resistance Voltage drop (IIII) and real power loss (II 2 RR) along the line Due to finite conductivity of the line Series inductance Series voltage drop, no real power loss Only self inductance (no mutual inductance) in balanced systems Shunt conductance Real power loss (VV 2 GG) Leakage current due to corona effects or leakage at insulators Typically neglected for overhead lines Shunt capacitance Capacitance to other conductors and to ground Line-charging currents

5 5 Conductors

6 Conductors 6 Before getting into transmission line models, we ll take a look at the conductors themselves Aluminum is the most common conductor Good conductivity Light weight Low cost Plentiful supply Most common cable type combines aluminum and steel Aluminum-conductor steel-reinforced (ACSR) Bare, stranded cable Core of steel strands provides strength Outer aluminum strands provide good conductivity

7 ACSR Cables 7 ACSR cables vary based on number of aluminum conductor strands and number of steel reinforcement strands ACSR variants assigned bird code names, e.g.: Dove: 26/7 Al/Steel stranding Bluebird: 84/19 Al/Steel stranding source: Glover, Sarma, Overbye Another increasingly popular cable type is all-aluminum-alloy conductor (AAAC) Stronger Lighter Higher conductivity More expensive

8 Cables 8 Cables are sized to provide the required current-carrying capability or ampacity Number of individual strands Diameter of individual strands Strand and cable diameter commonly measured in mils 1 mmmmmm = 0.001" Cross-sectional area often measured in circular mils or cmil Area of a circle with a diameter of dd = 1 mmmmmm = cccccccc = ππ = ssss iiii Area in cccccccc of a cable with diameter dd mmmmmm: AA = dd 2

9 ACSR Cable 9 Consider, for example, Falcon ACSR cable 54/19: 54 Al strands with a core of 19 steel strands Al strand diameter: 172 mmmmmm Al strand area: 172 mmmmmm 2 = kkkkkkkkkk Steel strand diameter: 103 mmmmmm Steel strand area: 103 mmmmmm 2 = kkkkkkkkkk Cable diameter: Cable area: 1545 mmmmmm 2 = 2387 kkkkkkkkkk Ampacity: 1380 AA Weight: 10,777 llll/mmmm

10 Bundling 10 In addition to increasing cable cross-sectional area, ampacity can be increased by adding additional cables to each phase bundling Two-, three-, and four-cable bundles are common:

11 Bundling 11 Typical bundling: 345 kv: two conductors 500 kv: three conductors 765 kv: four conductors Advantages of bundling: Lower resistance Lower reactance (inductance) Increased ampacity Reduced electric field gradient surrounding phase conductor Reduced corona Reduced loss, noise, and RF interference Improved heat dissipation

12 Insulators 12 Cables are supported by towers Must connect, while retaining electrical isolation Connections are typically made through ceramic or glass insulators High-voltage lines suspended by strings of insulator discs One or two strings Two prevents sway Number of discs dictated by line voltage, e.g.: 4-6 for 69 kv for 765 kv

13 Transposition 13 Transmission-line inductance and capacitance determined by geometry Cable size and relative spacing Consider three phases laid out side-by-side Phases a and c will have similar inductance and capacitance Inductance and capacitance of phase b will differ

14 Transposition 14 Transposition Switch the position of each phase twice along the length of the line Each phase occupies each position for one third of the line length Line remains balanced

15 15 Medium- and Short-Line Models

16 Short-Line Model 16 How we choose to model the electrical characteristics of a transmission line depends on the length of the line Short-line model: < ~80 kkkk Lumped model Account only for series impedance Neglect shunt capacitance RR and ωωωω are resistance and reactance per unit length, respectively Each with units of Ω/mm ll is the length of the line

17 Medium-Line Model 17 Medium-line model nominal-ππ model: 80 kkkk < ll < 250 kkkk Lumped model Now include shunt capacitance Still a lumped model zz = RR + jjjjjj Ω/mm and ZZ = zzzz Ω yy = ωωωω SS/mm and YY = yyyy SS All impedances and admittances lumped into one or two circuit components

18 Transmission Lines as Two-Port Networks 18 Before moving on to a model for longer transmission lines, we ll look at an alternative tool for characterizing transmission line networks We can treat transmission lines as general two-port networks As two-port networks, we can characterize transmission lines with their ABCD parameters or chain parameters

19 ABCD Parameters 19 ABCD (or chain or transmission or cascade) parameters define the following two-port relationships VV 1 = AAVV 2 + BBII 2 II 1 = CCVV 2 + DDII 2 In matrix form, the chain-parameter equations are VV 1 II 1 = AA BB CC DD AA, BB, CC, and DD are, in general, complex numbers AA and DD are dimensionless BB is an impedance with units of Ω CC is an admittance with units of SS VV 2 II 2 VV 1 and VV 2 are line-to-neutral voltages If the network is reciprocal, then AAAA BBBB = 1 If the network is symmetric, then AA = DD

20 ABCD Parameters Short-Line Model 20 We ll now derive the ABCD parameters for the shorttransmission-line model Applying KVL around the loop gives our first equation VV SS II RR ZZ VV RR = 0 So, VV SS = VV RR + ZZII RR AA = 1 and BB = ZZ

21 ABCD Parameters Short-Line Model 21 Applying KCL gives the second equation II ss = II RR and CC = 0 and DD = 1 The short-line ABCD matrix is AAAAAAAA = 1 ZZ 0 1 Note that, due to symmetry and reciprocity, AA = DD and AAAA BBBB = 1

22 ABCD Parameters Medium-Line Model 22 Next, for the medium-transmission-line model Applying KVL around the loop gives our first equation VV SS II RR + VV RR YY 2 ZZ VV RR = 0 VV SS = 1 + YYZZ 2 VV RR + ZZII RR This is the first chain parameter equation, where AA = 1 + YYYY 2 and BB = ZZ

23 ABCD Parameters Medium-Line Model 23 For the second equation, apply KCL at the sending end II ss VV ss YY 2 II RR VV RR YY 2 = 0 Substituting in our previous expression for VV SS II SS = VV RR YY 2 + II RR YYYY 2 II SS = 2 + YYYY 2 YY 2 VV RR + YYYY 2 II RR YY 2 VV RR YYYY 2 II RR This is the second chain-parameter equation, where CC = 1 + YYYY 4 YY and DD = 1 + YYYY 2

24 ABCD Parameters Medium-Line Model 24 The medium-line chain parameters are AAAAAAAA = 1 + YYZZ 2 ZZ 1 + YYYY 4 YY 1 + YYYY 2 Again, note that, due to symmetry and reciprocity, AA = DD and AAAA BBBB = 1 Also note that allowing YY 0 yields the chain parameters for the short-line model

25 Cascading Two-Port Networks 25 ABCD parameters or chain parameters are also called cascade parameters If we cascade multiple two-port networks, the ABCD parameter matrix for the cascade is the product of the individual ABCD parameter matrices AAAAAAAA = AA 1AA 2 + BB 1 CC 2 AA 1 BB 2 + BB 1 DD 2 CC 1 AA 2 + DD 1 CC 2 CC 1 BB 2 + DD 1 DD 2

26 Cascaded Two-Ports - Example 26 For example, consider the cascade of the following two two-port networks ABCD parameters for the first network are AAAAAADD 1 = And for the second network So the overall ABCD matrix is 1 + YY 1ZZ YY 1ZZ 1 4 AAAAAADD 2 = 1 ZZ 0 1 = 1 4 Ω 0 1 AAAAAAAA = ZZ 1 YY YY 1ZZ jjj 6 + jjjj Ω 4 + jjj SS 15 + jjjj = 1 + jjj 2 Ω 4 + jjj SS 1 + jjj

27 Cascaded Two-Ports - Example 27 If a sending-end voltage of VV SS = VV is applied, and no load is connected, what is the receiving-end voltage? VV SS = VV and II RR = 0 AA VV SS = AAVV RR + BBII RR = 1 + jjj VV RR The no-load receiving-end voltage is VV RR = jjj = 7.06 jjjj.2 VV VV RR = VV

28 Voltage Regulation 28 The voltage at the receiving end of a line will change depending on the load placed on the line Magnitude of this change is quantified as voltage regulation Voltage regulation: Change in receiving-end voltage from no load to full load, expressed as a percentage of the full-load voltage %VVVV = VV RRRRRR VV RRRRRR 100% VV RRRRRR Typically, transmission lines are designed to limit voltage regulation to about 10% As we ve seen, the no-load voltage is given by VV RRRRRR = VV SS AA

29 Voltage Regulation Example Consider a three-phase, 60 Hz, 345 kv transmission line with the following properties 200 km long zz = jjj.35 Ω/kkkk, yy = jjj.2 μμμμ/kkkk Full load is 700 MW at 95% of the rated voltage and a power factor of 0.99 leading Determine: ABCD parameters for an appropriate transmission-line model Phase shift between sending- and receiving-end voltages at full load Percent voltage regulation

30 Voltage Regulation Example Line is 200 km long, so a nominal-ππ model is appropriate where The ABCD parameters are ZZ = zz 200 kkkk = jjjj Ω YY = yy 200 kkkk = jjjjj μμμμ AAAAAAAA = 1 + YYZZ 2 ZZ 1 + YYYY 4 YY 1 + YYYY 2 = jjj jjjj Ω jjjjj μμμμ jjj.0027 AAAAAAAA = Ω μμμμ

31 Voltage Regulation Example At full load the line-to-line receiving-end voltage is VV RRRRRR = 345 kkkk 0.95 = kkvv LLLL And the line-to-neutral voltage is VV RRRRRR = kkvv LLLL 3 = kkvv LLLL Using the receiving-end voltage as the reference, the receiving-end voltage phasor is VV RR = kkkk We know that the load power is given by PP = 3VV RRRRRR II RR cos θθ θθ is the power-factor angle (leading, so it s negative) θθ = cos 1 pp. ff. = cos = 8.1

32 Voltage Regulation Example The receiving-end current phasor is II RR = PP 3VV RRRRRR cos θθ θθ = II RR = kkkk 700 MMMM kkkk To determine the phase shift from sending to receiving end, use chain parameters to determine VV SS (line-to-neutral) VV SS = AAVV RR + BBII RR VV SS = kkkk Ω kkkk VV SS = kkvv LN So, the phase shift along the line is 26.1

33 Voltage Regulation Example The percent voltage regulation is given by %VVVV = VV RRRRRR VV RRRRRR 100% VV RRRRRR The line-to-neutral no-load voltage is VV RRRRRR = VV SS AA = = kkkk The full-load line-to-neutral voltage was given to be VV RRRRRR = kkkk So, the percent voltage regulation is %VVVV = kkkk kkkk 100% = 8.7% kkkk

34 34 Exact Transmission-Line Equations

35 Distributed Transmission Line Model 35 The medium- and short-line models are lumped models All series impedance lumped into one element Shunt admittances lumped into two elements Real lines are distributed networks Lumped models are inaccurate for long lines To treat a line as a distributed network, consider the impedance and admittance of a segment of differential length, Δxx

36 Transmission Line Differential Equations 36 Apply KVL around the differential length of line VV xx + Δxx = VV xx + II xx zzδxx VV xx+δxx VV xx Δxx = zzii xx (1) If we let the length of the line segment, Δxx, go to zero, we get ddvv xx dddd = zzii xx (2) A first-order differential equation This is a second-order segment, so we need a second first-order differential equation to describe it completely Apply KCL at xx + Δxx II xx + Δxx = II xx + VV xx + Δxx yyδxx II xx+δxx II xx Δxx = yyvv xx + Δxx (3)

37 Transmission Line Differential Equations 37 Again, letting Δxx 0 ddii xx dddd = yyvv xx (4) Our goal is a single differential equation in VV xx to describe the segment of transmission line Must eliminate II xx Solving (2) for II xx and differentiating gives ddii xx dddd = 1 ZZ dd 2 VV xx ddxx 2 (5) Substituting (5) into (4) yields the single second-order differential equation for the line segment dd 2 VV xx ddxx 2 zzzzvv xx = 0 (6)

38 Transmission Line Differential Equations 38 dd 2 VV xx ddxx 2 zzzzvv xx = 0 (6) This is a second-order, homogeneous, linear, constant-coefficient, ordinary differential equation Its characteristic equation is ss 2 zzzz = 0 The roots of the characteristic polynomial are ss = ± zzzz = ±γγ where γγ = zzzz is the propagation constant, with units of mm 1 (or rrrrrr/mm) The solution to (6) is VV xx = KK 1 ee γγγγ + KK 2 ee γγγγ (7) where KK 1 and KK 2 are unknown constants to be determined through application of boundary conditions

39 Transmission Line Differential Equations 39 We can get an expression for current by differentiating (7) and substituting back into (2) Solving for II xx dddd xx dddd = γγkk 1ee γγγγ γγkk 2 ee γγγγ = zzii xx II xx = KK 1ee γγγγ KK 2 ee γγγγ zz γγ (8) The term in the denominator of (8) is the characteristic impedance of the line, ZZ cc, with units of ohms (Ω) ZZ cc = zz γγ = zz zzzz = zz yy (9)

40 Transmission Line Differential Equations 40 Using (9), (8) becomes II xx = KK 1ee γγγγ KK 2 ee γγγγ ZZ cc (10) We can now apply boundary conditions to determine the two unknown coefficients, KK 1 and KK 2 At the receiving end of the line, which we ll define to be xx = 0, we have So, VV 0 = VV RR and II 0 = II RR VV 0 = KK 1 + KK 2 = VV RR II 0 = KK 1 KK 2 ZZ cc = II RR

41 Transmission Line Differential Equations 41 Solving each equation for KK 2 KK 2 = VV RR KK 1 = KK 1 ZZ cc II RR Solving for KK 1, then back-substituting to solve for KK 2 gives KK 1 = VV RR+ZZ cc II RR 2 KK 2 = VV RR ZZ cc II RR 2 Substituting into (7) and (10) VV xx = II xx = VV RR+ZZ cc II RR 2 VV RR+ZZ cc II RR 2ZZ cc ee γγγγ + VV RR ZZ cc II RR 2 ee γγγγ (11) ee γγγγ VV RR ZZ cc II RR 2ZZ cc ee γγγγ (12)

42 Transmission Line Differential Equations 42 Collecting VV RR and II RR terms in (11) and (12) VV xx = eeγγγγ +ee γγγγ 2 VV RR + ZZ cc ee γγγγ ee γγγγ 2 II RR (13) II xx = 1 ZZ cc ee γγγγ ee γγγγ 2 VV RR + eeγγγγ +ee γγγγ 2 II RR (14) The terms in parentheses can be represented as hyperbolic functions VV xx = cosh γγγγ VV RR + ZZ cc sinh γγγγ II RR (15) II xx = 1 ZZ cc sinh γγγγ VV RR + cosh γγγγ II RR (16)

43 Transmission Line Differential Equations 43 Equations (15) and (16) give the chain parameters for the two-port network between a point at location xx along the line and the receiving end AAAAAAAA xx = cosh γγγγ 1 sinh γγγγ ZZ cc ZZ cc sinh γγγγ cosh γγγγ For chain parameters between sending and receiving ends, we set xx = ll AAAAAAAA = cosh γγll 1 sinh γγll ZZ cc ZZ cc sinh γγll cosh γγll

44 Propagation Constant 44 We defined the propagation constant as γγ = zzzz This is, in general, a complex value γγ = αα + jjjj (17) The real part, αα, is the attenuation constant Represents loss along the line Due to series resistance and/or shunt conductance The imaginary part, ββ, is the phase constant Represents change in phase along the line Due to series reactance and/or shunt susceptance

45 Long-Line Equivalent ππ Circuit 45 Now that we have exact ABCD parameters for a distributed transmission line, we can create an equivalent ππ circuit Here we re using ZZZ and YYY to distinguish from ZZ = zzzz and YY = yyyy of the lumped, nominal ππ-circuit model Equating the ABCD parameters with those for the equivalent ππ circuit above cosh γγγγ 1 sinh γγγγ ZZ cc ZZ cc sinh γγγγ cosh γγγγ = 1 + YY ZZ 2 YY 1 + YY ZZ 4 ZZZ 1 + YY ZZ 2

46 Long-Line Equivalent ππ Circuit 46 Equating the BB parameters, we see that ZZ = ZZ cc sinh γγγγ (18) Using (18) in the AA-parameter equation gives 1 + YY 2 ZZ cc sinh γγγγ = cosh γγγγ YY 2 = cosh γγγγ 1 ZZ cc sinh γγγγ = tanh γγγγ 2 ZZ cc The equivalent ππ circuit for long transmission lines (>250 km) is

47 Long-Line vs. Medium-Line Models 47 We can compare this equivalent ππ circuit with the nominal ππ circuit used for medium-length lines, where ZZ = zzzz and YY 2 = yy ll 2 Rewriting (18) using the definition for characteristic impedance, ZZ = zz yy sinh γγγγ = zzzz zz ZZ = zzzz ZZ = ZZ sinh γγγγ zzzz ll sinh γγγγ γγγγ yy sinh γγγγ We see that the series impedance of the long-line model is equal to that of the medium-line model, multiplied by a correction factor zzzz (20)

48 Long-Line vs. Medium-Line Models 48 Doing the same for the shunt admittance, we have YY γγγγ 2 2 = yy zz tanh = yyyy 2 yy zz tanh yyyy 2 γγγγ 2 YY = yyyy 2 2 tanh γγγγ 2 zzzz ll 2 YY 2 = YY 2 tanh γγγγ 2 γγγγ 2 Again, we see a similar correction factor relating the admittance, YY, of the lumped, nominal ππ circuit to the admittance of the distributed, equivalent ππ circuit, YYY

49 49 Lossless Lines

50 Lossless Lines 50 Transmission line models can be simplified significantly if we neglect loss Sacrifice accuracy for the sake of simplicity Series resistance, RR, and shunt conductance, GG, are the model parameters accounting for loss Let RR 0 and GG 0 (we ve already assumed GG = 0) Propagation constant for a lossless line is γγ = jjjj The attenuation constant is now zero, αα 0 γγ = zzzz = jjjjjj jjjjjj = jjjj LLLL = jjjj ββ = ωω LLLL

51 Lossless Lines ABCD Parameters 51 Using the propagation constant for a lossless line, the distributed model chain parameters become AA xx = DD xx = cosh jjjjjj = eejjjjjj + ee jjjjjj AA xx = DD xx = cos ββββ BB xx = ZZ cc sinh jjjjjj = ZZ cc ee jjjjjj ee jjjjjj BB xx = jjzz cc sin ββββ CC xx = 1 ZZ cc sinh jjjjjj = 1 ZZ cc ee jjjjjj ee jjjjjj sin ββββ CC xx = jj ZZ cc 2 2 2

52 Lossless Lines ABCD Parameters 52 Chain parameters at a distance xx from the end of a lossless line are AAAAAAAA xx = cos ββββ sin ββββ jj ZZ cc jjzz cc sin ββββ cos ββββ And at the sending end of a line of length ll, xx ll, and we have AAAAAAAA = cos ββll sin ββll jj ZZ cc jjzz cc sin ββll cos ββll The characteristic impedance of the lossless line is called the surge impedance ZZ cc = zz yy = jjjjjj jjjjjj = LL CC

53 Equivalent ππ Circuit Lossless Line 53 For the lossless line so, γγ = jjjj ZZ = ZZ cc sinh jjjjjj = jj LL sin ββββ = jjxx CC and, YY 2 = tanh ZZ cc jjjjjj 2 = jj tan ββββ 2 ZZ cc

54 Wavelength 54 The voltage along the lossless line is VV xx = AA xx VV RR + BB xx II RR VV xx = cos ββββ VV RR + jjzz cc sin ββββ II RR A wavelength, λλ, is the distance required for a phase shift of 360 along the line There is a 360 phase shift when xx = λλ and ββββ = 2ππ The wavelength is λλ = 2ππ ββ = 2ππ ωω LLLL = 1 ff LLLL = νν ff where νν = 1/ LLLL is the propagation velocity along the line

55 Wavelength 55 For overhead transmission lines, νν cc mm/ss That is, electrical waves propagate along the line at roughly the speed of light At 60 Hz, the wavelength is λλ = νν ff = = 5000 kkkk This is approximately the distance across the U.S. Most transmission lines are significantly shorter than a wavelength

56 Surge Impedance Loading (SIL) 56 Surge impedance loading (SIL) The power delivered by a transmission line to a resistive load whose impedance is equal to the surge impedance, ZZ cc, of that transmission line At SIL, the load current is II RR = VV RR ZZ cc The voltage along the line is VV xx = cos ββββ VV RR + jjzz cc sin ββββ II RR VV xx = cos ββββ VV RR + jjzz cc sin ββββ VV RR ZZ cc VV xx = VV RR cos ββββ + jj sin ββββ VV xx = VV RR ββββ Note that at SIL, the magnitude of the voltage is constant along the line A flat voltage profile

57 Surge Impedance Loading (SIL) 57 At SIL, the current along the line is given by II xx = jj sin ββββ ZZ cc VV RR + cos ββββ VV RR ZZ cc II xx = VV RR ZZ cc cos ββββ + jj sin ββββ II xx = VV RR ZZ cc ββββ The complex power along the line is At SIL SS xx = VV xx II xx = VV RR ββββ SS xx = VV RR 2 ZZ cc = PP xx + jjjj xx Power flow is independent of position along the line Reactive power is zero VV RR ZZ cc ββββ

58 Surge Impedance Loading (SIL) 58 Surge impedance loading is typically defined in terms of a transmission line s rated voltage SSSSSS = VV 2 rrrrrrrrrr ZZ cc At SIL, we ve seen that the voltage profile along a transmission line is flat At no load, II RR = 0, and the voltage is given by The source voltage is VV xx = cos ββββ VV RRRRRR VV SS = cos ββββ VV RRRRRR So the receiving-end voltage in terms of the sending-end voltage is VV RRRRRR = VV SS cos ββββ

59 Surge Impedance Loading (SIL) 59 The no-load receiving-end voltage is VV RRRRRR = VV SS cos ββββ As long as ββββ ππ/2, i.e. ll λλ/4, Voltage will increase along the length of the line No-load receiving-end voltage is greater than the sending-end voltage Voltage regulation worsens with increasing line length source: Glover, Sarma, Overbye

60 Real Power vs. Voltage Angle 60 Assume a voltage angle between the sending and receiving ends of a lossless line of δδ VV RR = VV RR 0 and VV SS = VV SS δδ Using the equivalent ππ network for the lossless line, we can determine the receiving-end current Applying KCL at the receiving end II RR = VV SS VV RR jjxx jj BB 2 VV RR II RR = VV SS δδ VV RR 0 jjxx jj BB 2 VV RR 0

61 Real Power vs. Voltage Angle 61 The complex power at the load is SS RR = VV RR II RR = VV RRVV SS δδ VV RR 2 SS RR = jj VV RRVV SS δδ XX jjxx jj VV 2 RR BB + jj XX 2 VV RR 2 + jj BB 2 VV RR 2 SS RR = jj VV RRVV SS XX cos δδ + jj sin δδ jj VV 2 RR BB + jj XX 2 VV RR 2 SS RR = VV RRVV SS XX The real power delivered is sin δδ + jj VV RRVV SS XX cos δδ VV 2 RR XX + BB 2 VV RR 2 PP RR = PP SS = Re SS RR = VV RRVV SS XX sin δδ

62 Power Flow Lossless Lines 62 The delivered power is a function of the voltage phase shift along the line, δδ PP RR = VV RRVV SS XX sin δδ For the lossless line the series reactance is XX = ZZ cc sin(ββββ) so, PP RR = VV RRVV SS VV sin δδ = ZZ cc sin(ββββ) RR VV SS ZZ cc sin 2ππππ λλ sin δδ

63 Power Flow Lossless Lines 63 Converting VV RR and VV SS to per unit PP RR = VV RR VV rrrrrrrrrr VV SS VV rrrrrrrrrr 2 VV rrrrrrrrrr ZZ cc sin 2ππππ λλ sin δδ PP RR = VV RR,pppp VV SS,pppp 2 VV rrrrrrrrrr ZZ cc sin δδ sin 2ππππ λλ The term in parentheses is SIL, so PP RR = VV RR,pppp VV SS,pppp SSSSSS sin δδ sin 2ππππ λλ This provides a relationship between: Power delivered over a transmission line Voltage drop along the line Power angle

64 Maximum Power Flow Lossless Lines 64 PP RR = VV RR VV SS ZZ cc sin 2ππππ λλ sin δδ = VV RR,pppp VV SS,pppp SSSSSS sin δδ sin 2ππππ λλ The delivered power is a function of the voltage phase shift along the line Maximum power occurs when δδ = 90 PP mmmmmm = VV RR VV SS ZZ cc sin 2ππππ λλ = VV RR,ppppVV SS,pppp SSSSSS sin 2ππππ λλ The steady-state stability limit of a line

65 Steady-State Stability Limit 65 PP mmmmmm = VV RR VV SS ZZ cc sin 2ππππ λλ = VV RR,ppppVV SS,pppp SSSSSS sin 2ππππ λλ This maximum power is the steady-state stability limit of a transmission line Loads exceeding this limit will result in a loss of synchronism at the receiving end Synchronous machines at the sending and receiving ends will fall out of synchronization Steady-state stability limit proportional to Inverse of line length Square of the line voltage

66 Transmission Line Loadability 66 Three primary factors limit power flow over transmission lines: Phase shift Voltage drop Thermal limit Relevant limit depends on line length Phase shift: Proportional to line length and power flow Phase shift places a stability limit on power flow Exceeding PP mmmmmm (δδ = 90 ) results in loss of synchronism For satisfactory transient stability, typically δδ Stability limits the loadability of long transmission lines (>150 mi)

67 Transmission Line Loadability 67 Voltage drop: Voltage drop along a line is also proportional to line length and power flow Typically, voltage drop limited to 5% 10% Voltage drop limits power flow on medium-length lines (50mi 150 mi) Thermal limits As power flow increases, line temperature increases As temperature increases, lines sag and loose tensile strength A line s thermal limit is independent of line length Thermal limits dominate for short lines (<50 mi)

68 Transmission Line Loadability 68 Comparison of theoretical and practical loadability limits Practical limit assumes: VV RR /VV ss 0.95 δδ source: Glover, Sarma, Overbye

69 Practical Line Loadability Example 69 Determine how much power that can be transmitted over a 400 km, 500 kv transmission line, given the following: Voltage drop along the line limited to 10% Power angle limited to δδ mmmmmm = 30 The characteristic impedance of the line is ZZ cc = 280Ω Assume VV SS,pppp = 1.0 pp. uu. Power delivered to the receiving end of the line is PP RR = VV RR,pppp VV SS,pppp SSSSSS sin δδ sin 2ππππ λλ PP RR = SSSSSS sin sin 30 2ππ 400 kkkk 5000 kkkk

70 Practical Line Loadability Example 70 In terms of SIL, the power the line can deliver is PP RR = SSSSSS Surge impedance loading for the line is so, SSSSSS = VV 2 rrrrrrrrrr = ZZ cc 500 kkkk Ω PP RR = MMMM = MMMM PP RR = 834 MMMM

71 71 Reactive Compensation

72 Reactive Compensation 72 Voltage profile and loadability of a transmission line depend on relative line and load impedances By varying line impedance, we can affect voltage regulation and line loadability Add shunt or series reactance to the line reactive compensation Types of reactive compensation Shunt reactors (inductors) Absorb reactive power Reduce receiving-end voltage under light load Must be removed under higher-load conditions Shunt capacitors Supply reactive power Increase receiving-end voltage at full load Removed under light-load conditions

73 Reactive Compensation 73 Types of reactive compensation (cont d) Series capacitors Reduce series line impedance Reduce line voltage drops Increase steady-state stability limit Static VAR compensators (SVCs) Thyristor-controlled shunt reactors and capacitors Automatically adjust compensation depending on load

74 Reactive Compensation 74 Amount of reactive compensation is typically expressed as a percentage of line impedance For example, the circuit above shows a transmission line with NNNNN shunt reactive compensation

75 Reactive Compensation Example Consider a 300 km, 765 kv, three-phase transmission line with the following chain parameters: AA = BB = ZZ = Shunt reactors, switched in during light-load conditions only, provide 75% compensation Full-load current is 1.9 ka at 730 kv with unity power factor The sending-end voltage, VV SS, is constant Determine: %VVVV of the uncompensated line %VVVV of the compensated line

76 Reactive Compensation Example Full-load, line-to-neutral, receiving-end voltage, using it as the 0 phase reference: VV RRRRRR = kkkk = kkkk Use chain parameters to determine the sending-end voltage, VV SS VV SS = AAVV RRRRRR + BBII RRRRRR VV SS = ( kkkk) Ω VV SS = kkkk The no-load, line-to-neutral, receiving-end voltage is VV RRRRRR = VV SS AA = kkkk = kkkk Percent voltage regulation for the uncompensated line is kkkk %VVVV = VV RRRRRR VV RRRRRR VV RRRRRR 100% = kkkk kkkk kkkk 100% %VVVV = 12.7%

77 Reactive Compensation Example For the compensated line, we need to calculate new chain parameters Shunt admittance of the uncompensated line can be determined from the known chain parameters where So, AA = = 1 + YY ZZ ZZ = BB = Ω YY = AA 1 2 ZZ = Ω YY = SS YY = jjj SS 2

78 Reactive Compensation Example After adding compensation, the equivalent shunt susceptance decreases by 75% YY eeee = jjj SS 0.25 YY eeee = jjjjj 10 6 SS Use YY eeee to calculate the AA parameter for the compensated line AA eeee = 1 + YY eeeezz 2 = Note that shunt reactive compensation does not affect the series impedance, ZZZ, and therefor does not affect BB

79 Reactive Compensation Example The no-load receiving-end voltage for the compensated line: VV RRRRRR = VV SS AA eeee = kkkk VV RRRRLL = kkkk Percent voltage regulation for the compensated line is %VVVV = VV RRRRRR VV RRRRRR 100% VV RRRRRR %VVVV = kkkk kkkk kkkk 100% %VVVV = 6.8% Reactive compensation has improved voltage regulation from 12.7% to 6.8%

EE 340 Transmission Lines. Spring 2012

EE 340 Transmission Lines. Spring 2012 EE 340 Transmission Lines Spring 2012 Physical Characteristics Overhead lines An overhead transmission line usually consists of three conductors or bundles of conductors containing the three phases of

More information

EE 340 Transmission Lines

EE 340 Transmission Lines EE 340 Transmission Lines Physical Characteristics Overhead lines An overhead transmission line usually consists of three conductors or bundles of conductors containing the three phases of the power system.

More information

EE 740 Transmission Lines

EE 740 Transmission Lines EE 740 Transmission Lines 1 High Voltage Power Lines (overhead) Common voltages in north America: 138, 230, 345, 500, 765 kv Bundled conductors are used in extra-high voltage lines Stranded instead of

More information

Transmission Line Models Part 1

Transmission Line Models Part 1 Transmission Line Models Part 1 Unlike the electric machines studied so far, transmission lines are characterized by their distributed parameters: distributed resistance, inductance, and capacitance. The

More information

Fatima Michael college of Engineering and Technology

Fatima Michael college of Engineering and Technology Fatima Michael college of Engineering and Technology DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EE2303 TRANSMISSION AND DISTRIBUTION SEM: V Question bank UNIT I INTRODUCTION 1. What is the electric

More information

EE 741. Primary & Secondary Distribution Systems

EE 741. Primary & Secondary Distribution Systems EE 741 Primary & Secondary Distribution Systems Radial-Type Primary Feeder Most common, simplest and lowest cost Example of Overhead Primary Feeder Layout Example of Underground Primary Feeder Layout Radial-Type

More information

Diode Circuits Recent GATE Problems

Diode Circuits Recent GATE Problems Diode Circuits Recent GATE Problems 1. The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode DD 1 is CC 1 DD 2 cos(ωωωω) AC DD 1 CC 1 (a) cos(ωωωω) 1 (b) sin(ωωωω)

More information

Exercises on overhead power lines (and underground cables)

Exercises on overhead power lines (and underground cables) Exercises on overhead power lines (and underground cables) 1 From the laws of Electromagnetism it can be shown that l c = 1 v 2 where v is the speed of propagation of electromagnetic waves in the environment

More information

Q. 1 Q. 25 carry one mark each.

Q. 1 Q. 25 carry one mark each. Q. Q. 25 carry one mark each. Q. A random variable XX has probability density function ff(xx) as given below: aa bbbb ffffff 0 < xx < ff(xx) = 0 otherwise If the expected value EE[XX] = 2/3, then PPPP[XX

More information

b) discrete-time iv) aperiodic (finite energy)

b) discrete-time iv) aperiodic (finite energy) EE 464 Frequency Analysis of Signals and Systems Fall 2018 Read Text, Chapter. Study suggestion: Use Matlab to plot several of the signals and their DTFT in the examples to follow. Some types of signal

More information

Introduction to Harmonic Analysis Basics

Introduction to Harmonic Analysis Basics Introduction to Harmonic Analysis Basics Course No: E05-009 Credit: 5 PDH Velimir Lackovic, Char. Eng. Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980 P: (877) 322-5800

More information

Homework Assignment Consider the circuit shown. Assume ideal op-amp behavior. Which statement below is true?

Homework Assignment Consider the circuit shown. Assume ideal op-amp behavior. Which statement below is true? Question 1 (2 points each unless noted otherwise) Homework Assignment 03 1. Consider the circuit shown. Assume ideal op-amp behavior. Which statement below is true? (a) V = VV + = 5 V (op-amp operation)

More information

Chapter 10: Compensation of Power Transmission Systems

Chapter 10: Compensation of Power Transmission Systems Chapter 10: Compensation of Power Transmission Systems Introduction The two major problems that the modern power systems are facing are voltage and angle stabilities. There are various approaches to overcome

More information

Lab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters

Lab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters Lab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters Goal: In circuits with a time-varying voltage, the relationship between current and voltage is more complicated

More information

PRELIMINARIES. Generators and loads are connected together through transmission lines transporting electric power from one place to another.

PRELIMINARIES. Generators and loads are connected together through transmission lines transporting electric power from one place to another. TRANSMISSION LINES PRELIMINARIES Generators and loads are connected together through transmission lines transporting electric power from one place to another. Transmission line must, therefore, take power

More information

Microphonics. T. Powers

Microphonics. T. Powers Microphonics T. Powers What is microphonics? Microphonics is the time domain variation in cavity frequency driven by external vibrational sources. A 1.5 GHz structure 0.5 m long will change in frequency

More information

Accurate Power Conversion Measurements on High Power Motor Drives. Presented by: Ian Walker GMW Associates

Accurate Power Conversion Measurements on High Power Motor Drives. Presented by: Ian Walker GMW Associates Accurate Power Conversion Measurements on High Power Motor Drives Presented by: Ian Walker GMW Associates ian@gmw.com Motor & Drive Systems; January 21, 2016 Interconnections for the test of a low power

More information

PATCH ANTENNA DESIGN

PATCH ANTENNA DESIGN FACULTY OF ELECTRONICS, TELECOMMUNICATIONS, AND INFORMATION TECHNOLOGY Department of Telecommunications and Information Technology Laboratory of Antennas and Propagation Prof. dr. ing. Ion BOGDAN PATCH

More information

Power System Analysis Prof. A. K. Sinha Department of Electrical Engineering Indian institute of Technology, Kharagpur

Power System Analysis Prof. A. K. Sinha Department of Electrical Engineering Indian institute of Technology, Kharagpur Power System Analysis Prof. A. K. Sinha Department of Electrical Engineering Indian institute of Technology, Kharagpur Lecture - 10 Transmission Line Steady State Operation Voltage Control (Contd.) Welcome

More information

Student s Copy. Geometry Unit 2. Similarity, Proof, and Trigonometry. Eureka Math. Eureka Math

Student s Copy. Geometry Unit 2. Similarity, Proof, and Trigonometry. Eureka Math. Eureka Math Student s Copy Geometry Unit 2 Similarity, Proof, and Trigonometry Eureka Math Eureka Math Lesson 1 Lesson 1: Scale Drawings Triangle AAAAAA is provided below, and one side of scale drawing AA BB CC is

More information

If You Give A Mouse A Letter He ll Want The Whole Alphabet By

If You Give A Mouse A Letter He ll Want The Whole Alphabet By If You Give A Mouse A Letter He ll Want The Whole Alphabet By a TeachWithMe.com A If you give a mouse an A he will want a Bb. AAAA aaaa B If you give a mouse an B he will want a Cc. BBBB bbbb C If you

More information

THE ELECTRICAL CHARACTERISTICS OF LONG

THE ELECTRICAL CHARACTERISTICS OF LONG Active and Passive Elec. Comp.. 1990, Vol. 14, pp. 17-23 Reprints available directly from the publisher Photocopying permitted by license only (C) 1990 Gordon and Breach Science Publishers, Inc. Printed

More information

AUTOMATIC REACTIVE POWER COMPENSATOR: AN OPEN LOOP APPROACH

AUTOMATIC REACTIVE POWER COMPENSATOR: AN OPEN LOOP APPROACH AUTOMATIC REACTIVE POWER COMPENSATOR: AN OPEN LOOP APPROACH A thesis submitted for the degree of Master of Philosophy by Abdul-Majeed RAHIM School of Engineering and Design Brunel University May 2010 1

More information

AC Power Instructor Notes

AC Power Instructor Notes Chapter 7: AC Power Instructor Notes Chapter 7 surveys important aspects of electric power. Coverage of Chapter 7 can take place immediately following Chapter 4, or as part of a later course on energy

More information

EL 403 MODEL TEST PAPER - 1 POWER SYSTEMS. Time: Three Hours Maximum Marks: 100

EL 403 MODEL TEST PAPER - 1 POWER SYSTEMS. Time: Three Hours Maximum Marks: 100 POWER SYSTEMS Time: Three Hours Maximum Marks: 0 Answer five questions, taking ANY TWO from Group A, any two from Group B and all from Group C. All parts of a question (a, b, etc. ) should be answered

More information

Ballast Resistance Measurement Theory and Practice

Ballast Resistance Measurement Theory and Practice Ballast Resistance Measurement Theory and Practice Stuart Landau, PE, MIRSE Signal and Train Control Engineer CH2M 119 Cherry Hill Road, Suite 300 Parsippany, NJ 07054 Stuart.Landau@ch2m.com 4,120 words

More information

Roll No. :... Invigilator s Signature :.. CS/B.TECH(EE)/SEM-5/EE-502/ POWER SYSTEM-I. Time Allotted : 3 Hours Full Marks : 70

Roll No. :... Invigilator s Signature :.. CS/B.TECH(EE)/SEM-5/EE-502/ POWER SYSTEM-I. Time Allotted : 3 Hours Full Marks : 70 Name : Roll No. :.... Invigilator s Signature :.. CS/B.TECH(EE)/SEM-5/EE-502/2011-12 2011 POWER SYSTEM-I Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates

More information

Department of Electronics &Electrical Engineering

Department of Electronics &Electrical Engineering Department of Electronics &Electrical Engineering Question Bank- 3rd Semester, (Network Analysis & Synthesis) EE-201 Electronics & Communication Engineering TWO MARKS OUSTIONS: 1. Differentiate between

More information

Impedance Measurement Handbook

Impedance Measurement Handbook Impedance Measurement Handbook 1st edition 1 Introduction This handbook describes settings and precautions that apply when using an impedance measuring instrument. Impedance Measurement Handbook 1 Making

More information

UNIT 1 CIRCUIT ANALYSIS 1 What is a graph of a network? When all the elements in a network is replaced by lines with circles or dots at both ends.

UNIT 1 CIRCUIT ANALYSIS 1 What is a graph of a network? When all the elements in a network is replaced by lines with circles or dots at both ends. UNIT 1 CIRCUIT ANALYSIS 1 What is a graph of a network? When all the elements in a network is replaced by lines with circles or dots at both ends. 2 What is tree of a network? It is an interconnected open

More information

In Class Examples (ICE)

In Class Examples (ICE) In Class Examples (ICE) 1 1. A 3φ 765kV, 60Hz, 300km, completely transposed line has the following positive-sequence impedance and admittance: z = 0.0165 + j0.3306 = 0.3310 87.14 o Ω/km y = j4.67 410-6

More information

Arc Flash Hazard Calculations in DC Systems

Arc Flash Hazard Calculations in DC Systems Arc Flash Hazard Calculations in DC Systems Course No: E03-035 Credit: 3 PDH Velimir Lackovic, Char. Eng. Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980 P: (877)

More information

Lab 1. Objectives. Single Line Diagram. Methodology. Observations. Jon Jawnsy Yu 26 October 2009

Lab 1. Objectives. Single Line Diagram. Methodology. Observations. Jon Jawnsy Yu 26 October 2009 Lab 1 Objectives In this lab, our objective is to simulate a simple single machine infinite bus configuration using the PowerWorld Simulator software. We design a local generator system (a synchronous

More information

4. Differential Amplifiers. Electronic Circuits. Prof. Dr. Qiuting Huang Integrated Systems Laboratory

4. Differential Amplifiers. Electronic Circuits. Prof. Dr. Qiuting Huang Integrated Systems Laboratory 4. Differential Amplifiers Electronic Circuits Prof. Dr. Qiuting Huang Integrated Systems Laboratory Differential Signaling Basics and Motivation Transmitting information with two complementary signals

More information

Electrical Power Systems

Electrical Power Systems Electrical Power Systems CONCEPT, THEORY AND PRACTICE SECOND EDITION SUBIR RAY Professor MVJ College of Engineering Bangalore PHI Learning Pfcte tofm Delhi-110092 2014 Preface xv Preface to the First Edition

More information

What is Corona Effect in Power System and Why it Occurs?

What is Corona Effect in Power System and Why it Occurs? Corona Effect in Power System Electric power transmission practically deals in the bulk transfer of electrical energy, from generating stations situated many kilometers away from the main consumption centers

More information

CHAPTER 9. Sinusoidal Steady-State Analysis

CHAPTER 9. Sinusoidal Steady-State Analysis CHAPTER 9 Sinusoidal Steady-State Analysis 9.1 The Sinusoidal Source A sinusoidal voltage source (independent or dependent) produces a voltage that varies sinusoidally with time. A sinusoidal current source

More information

Determination of Optimal Account and Location of Series Compensation and SVS for an AC Transmission System

Determination of Optimal Account and Location of Series Compensation and SVS for an AC Transmission System ISSN (e): 2250 3005 Vol, 04 Issue, 5 May 2014 International Journal of Computational Engineering Research (IJCER) Determination of Optimal Account and Location of Series Compensation and SVS for an AC

More information

ELEC351 Lecture Notes Set 1

ELEC351 Lecture Notes Set 1 ELEC351 Lecture Notes Set 1 There is a tutorial on Monday September 10! You will do the first workshop problem in the tutorial. Bring a calculator. The course web site is: www.ece.concordia.ca/~trueman/web_page_351.htm

More information

Useful Information Master Copy

Useful Information Master Copy Useful Information Master Copy 1of10 Pantograph Ratio and Cutter Selection SINGLE LINE COPY SOLID SUNK COPY COPY MASTER HEIGHT OVERALL HEIGHT LINE WIDTH OVERALL HEIGHT The relationship between line width

More information

Level 6 Graduate Diploma in Engineering Electrical Energy Systems

Level 6 Graduate Diploma in Engineering Electrical Energy Systems 9210-114 Level 6 Graduate Diploma in Engineering Electrical Energy Systems Sample Paper You should have the following for this examination one answer book non-programmable calculator pen, pencil, ruler,

More information

III/IV B.Tech (Regular/Supplementary) DEGREE EXAMINATION

III/IV B.Tech (Regular/Supplementary) DEGREE EXAMINATION Hall Ticket Number: 14EE503 October, 2018 Fifth Semester Time: Three Hours Answer Question No.1 compulsorily. Answer ONE question from each unit. III/IV B.Tech (Regular/Supplementary) DEGREE EXAMINATION

More information

ISSN: International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) Volume 2, No 5, May 2013

ISSN: International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) Volume 2, No 5, May 2013 750kv Transmission Line parameter and line Efficiency calculation and the performance of High Voltage alternating current Transmission system using MATLAB program Alka Szeerin Mansoori M.E. Student of

More information

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK SUBJECT CODE & NAME : EE 1402 HIGH VOLTAGE ENGINEERING UNIT I

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK SUBJECT CODE & NAME : EE 1402 HIGH VOLTAGE ENGINEERING UNIT I DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK SUBJECT CODE & NAME : EE 1402 HIGH VOLTAGE ENGINEERING YEAR / SEM : IV / VII UNIT I OVER VOLTAGES IN ELECTRICAL POWER SYSTEMS 1. What

More information

Transmission Lines. Ranga Rodrigo. January 13, Antennas and Propagation: Transmission Lines 1/46

Transmission Lines. Ranga Rodrigo. January 13, Antennas and Propagation: Transmission Lines 1/46 Transmission Lines Ranga Rodrigo January 13, 2009 Antennas and Propagation: Transmission Lines 1/46 1 Basic Transmission Line Properties 2 Standing Waves Antennas and Propagation: Transmission Lines Outline

More information

Transmission of Electrical Energy

Transmission of Electrical Energy Transmission of Electrical Energy Electrical energy is carries by conductors such as overhead transmission lines and underground cables. The conductors are usually aluminum cable steel reinforced (ACSR),

More information

Analysis and Comparison of Speed Control of DC Motor using Sliding Mode Control and Linear Quadratic Regulator

Analysis and Comparison of Speed Control of DC Motor using Sliding Mode Control and Linear Quadratic Regulator ISSN: 2349-253 Analysis and Comparison of Speed Control of DC Motor using Sliding Mode Control and Linear Quadratic Regulator 1 Satyabrata Sahoo 2 Gayadhar Panda 1 (Asst. Professor, Department of Electrical

More information

CDS 101/110: Lecture 9.1 Frequency DomainLoop Shaping

CDS 101/110: Lecture 9.1 Frequency DomainLoop Shaping CDS /: Lecture 9. Frequency DomainLoop Shaping November 3, 6 Goals: Review Basic Loop Shaping Concepts Work through example(s) Reading: Åström and Murray, Feedback Systems -e, Section.,.-.4,.6 I.e., we

More information

Course ELEC Introduction to electric power and energy systems. Additional exercises with answers December reactive power compensation

Course ELEC Introduction to electric power and energy systems. Additional exercises with answers December reactive power compensation Course ELEC0014 - Introduction to electric power and energy systems Additional exercises with answers December 2017 Exercise A1 Consider the system represented in the figure below. The four transmission

More information

Waveguides. Metal Waveguides. Dielectric Waveguides

Waveguides. Metal Waveguides. Dielectric Waveguides Waveguides Waveguides, like transmission lines, are structures used to guide electromagnetic waves from point to point. However, the fundamental characteristics of waveguide and transmission line waves

More information

Modeling and Simulation of Load Frequency Control for Three Area Power System Using Proportional Integral Derivative (PID) Controller

Modeling and Simulation of Load Frequency Control for Three Area Power System Using Proportional Integral Derivative (PID) Controller American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-441, ISSN (Online) 2313-442 Global Society of Scientific Research and Researchers http://asrjetsjournal.org/

More information

Summary Paper for C IEEE Guide for Application of Digital Line Current Differential Relays Using Digital Communication

Summary Paper for C IEEE Guide for Application of Digital Line Current Differential Relays Using Digital Communication Summary Paper for C37.243 IEEE Guide for Application of Digital Line Current Differential Relays Using Digital Communication by: Neftaly Torres, P.E. 70 th Annual Conference for Protective Relay Engineers,

More information

Chapter 12: Transmission Lines. EET-223: RF Communication Circuits Walter Lara

Chapter 12: Transmission Lines. EET-223: RF Communication Circuits Walter Lara Chapter 12: Transmission Lines EET-223: RF Communication Circuits Walter Lara Introduction A transmission line can be defined as the conductive connections between system elements that carry signal power.

More information

Transmission Line Transient Overvoltages (Travelling Waves on Power Systems)

Transmission Line Transient Overvoltages (Travelling Waves on Power Systems) Transmission Line Transient Overvoltages (Travelling Waves on Power Systems) The establishment of a potential difference between the conductors of an overhead transmission line is accompanied by the production

More information

Scattered thoughts on Scattering Parameters By Joseph L. Cahak Copyright 2013 Sunshine Design Engineering Services

Scattered thoughts on Scattering Parameters By Joseph L. Cahak Copyright 2013 Sunshine Design Engineering Services Scattered thoughts on Scattering Parameters By Joseph L. Cahak Copyright 2013 Sunshine Design Engineering Services Scattering parameters or S-parameters (aka Spars) are used by RF and microwave engineers

More information

1 Introduction General Background The New Computer Environment Transmission System Developments Theoretical Models and Computer Programs

1 Introduction General Background The New Computer Environment Transmission System Developments Theoretical Models and Computer Programs Modeling Techniques in Power Systems 1 General Background The New Computer Environment Transmission System Developments Theoretical Models and Computer Programs 2 Transmission Systems Linear Transformation

More information

ANGLE MODULATION. U1. PHASE AND FREQUENCY MODULATION For angle modulation, the modulated carrier is represented by

ANGLE MODULATION. U1. PHASE AND FREQUENCY MODULATION For angle modulation, the modulated carrier is represented by [4.1] ANGLE MODULATION U1. PHASE AND FREQUENCY MODULATION For angle modulation, the modulated carrier is represented by xx cc (tt) = AA cccccc[ωω cc tt + φφ(tt)] (1.1) Where A ω c are constants the phase

More information

MAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPALLI UNIT II TRANSMISSION LINE PARAMETERS

MAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPALLI UNIT II TRANSMISSION LINE PARAMETERS Part A (2 Marks) UNIT II TRANSMISSION LINE PARAMETERS 1. When does a finite line appear as an infinite line? (Nov / Dec 2011) It is an imaginary line of infinite length having input impedance equal to

More information

RF Cavity Design. 1 Introduction the outline of a general cavity design procedure. E. Jensen CERN, Geneva, Switzerland

RF Cavity Design. 1 Introduction the outline of a general cavity design procedure. E. Jensen CERN, Geneva, Switzerland RF Cavity Design E. Jensen CERN, Geneva, Switzerland Abstract After a short overview of a general approach to cavity design, we sketch the derivation of waveguide modes from plane waves and of cavity fields

More information

EC Transmission Lines And Waveguides

EC Transmission Lines And Waveguides EC6503 - Transmission Lines And Waveguides UNIT I - TRANSMISSION LINE THEORY A line of cascaded T sections & Transmission lines - General Solution, Physical Significance of the Equations 1. Define Characteristic

More information

EE2022 Electrical Energy Systems

EE2022 Electrical Energy Systems EE0 Electrical Energy Systems Lecture : Transformer and Per Unit Analysis 7-0-0 Panida Jirutitijaroen Department of Electrical and Computer Engineering /9/0 EE0: Transformer and Per Unit Analysis by P.

More information

TRANSMISSION LINE 1. Instructed by: Miss. R T Gunasekara

TRANSMISSION LINE 1. Instructed by: Miss. R T Gunasekara TRANSMISSION LINE 1 Instructed by: Miss. R T Gunasekara Name :- D.K.Pathirana Index No :- 080332P Group :- EE9 Date of Per. :- 24/01/2011 Instructed by :- R.T.Gunasekara OBSEVATION SHEET Name :- D.K.Pathirana

More information

NH-67, TRICHY MAIN ROAD, PULIYUR, C.F , KARUR DT. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING COURSE MATERIAL

NH-67, TRICHY MAIN ROAD, PULIYUR, C.F , KARUR DT. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING COURSE MATERIAL NH-67, TRICHY MAIN ROAD, PULIYUR, C.F. 639 114, KARUR DT. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING COURSE MATERIAL Subject Name: Microwave Engineering Class / Sem: BE (ECE) / VII Subject

More information

ECE 422/522 Power System Operations & Planning/Power Systems Analysis II 5 - Reactive Power and Voltage Control

ECE 422/522 Power System Operations & Planning/Power Systems Analysis II 5 - Reactive Power and Voltage Control ECE 422/522 Power System Operations & Planning/Power Systems Analysis II 5 - Reactive Power and Voltage Control Spring 2014 Instructor: Kai Sun 1 References Saadat s Chapters 12.6 ~12.7 Kundur s Sections

More information

Microwave Circuits Design. Microwave Filters. high pass

Microwave Circuits Design. Microwave Filters. high pass Used to control the frequency response at a certain point in a microwave system by providing transmission at frequencies within the passband of the filter and attenuation in the stopband of the filter.

More information

EE3079 Experiment: Chaos in nonlinear systems

EE3079 Experiment: Chaos in nonlinear systems EE3079 Experiment: Chaos in nonlinear systems Background: November 2, 2016 Revision The theory of nonlinear dynamical systems and Chaos is an intriguing area of mathematics that has received considerable

More information

GATE 2014: General Instructions during Examination

GATE 2014: General Instructions during Examination GATE 2014: General Instructions during Examination 1. Total duration of the GATE examination is 180 minutes. 2. The clock will be set at the server. The countdown timer at the top right corner of screen

More information

ELC 131 CIRCUIT ANALYSIS I

ELC 131 CIRCUIT ANALYSIS I ELC 131 CIRCUIT ANALYSIS I COURSE DESCRIPTION: Prerequisites: None Corequisites: MAT 121 This course introduces DC and AC electricity with emphasis on circuit analysis, measurements, and operation of test

More information

SECTION 1 INTRODUCTION

SECTION 1 INTRODUCTION Power PE Engineering Pro Guides Full Exam 80 exam difficulty level problems and detailed solutions Tests concepts not tested by other sample exams. Follows the exam outline and covers the main topics.

More information

CHAPTER 2. Basic Concepts, Three-Phase Review, and Per Unit

CHAPTER 2. Basic Concepts, Three-Phase Review, and Per Unit CHAPTER 2 Basic Concepts, Three-Phase Review, and Per Unit 1 AC power versus DC power DC system: - Power delivered to the load does not fluctuate. - If the transmission line is long power is lost in the

More information

INTEGRATING POWERS OF TRIGONOMETRIC FUNCTIONS

INTEGRATING POWERS OF TRIGONOMETRIC FUNCTIONS INTEGRATING POWERS OF TRIGONOMETRIC FUNCTIONS We now consider four cases of integrals involving powers of sine and cosine. The method used in each case is shown by an illustration. CASE 1: sin nn xx dddd

More information

ANTENNAS AND PROPAGATION

ANTENNAS AND PROPAGATION TECHNICAL UNIVERSITY GHEORGHE ASACHI OF IAȘI FACULTY OF ELECTRONICS, TELECOMMUNICATIONS, AND INFORMATION TECHNOLOGY Prof. Ion BOGDAN Lecture notes on ANTENNAS AND PROPAGATION 017 C O N T E N T 1. FUNDAMENTALS

More information

Cavity Testing Mathematics. Tom Powers USPAS SRF Testing Course 19 Jan. 2014

Cavity Testing Mathematics. Tom Powers USPAS SRF Testing Course 19 Jan. 2014 Cavity Testing Mathematics Tom Powers USPAS SRF Testing Course 19 Jan. 014 General Block Diagram for Vertical or Horizontal Test Stand Frequency tracking source can be either a VCO-PLL based system or

More information

COURSE PLANNER SUBJECT: ELECTRICAL POWER SYSTEM II

COURSE PLANNER SUBJECT: ELECTRICAL POWER SYSTEM II COURSE PLANNER SUBJECT: ELECTRICAL POWER SYSTEM II [260908] B.E. Third Year Class Electrical 204 Term: 6/2 (DEC-6 to APR-7) Faculty: PROF. J. I. JARIWALA PROF. A. S. SHAH PROF. T. M. PANCHAL PROF. N. B.

More information

Implementing Re-Active Power Compensation Technique in Long Transmission System (750 Km) By Using Shunt Facts Control Device with Mat Lab Simlink Tool

Implementing Re-Active Power Compensation Technique in Long Transmission System (750 Km) By Using Shunt Facts Control Device with Mat Lab Simlink Tool Implementing Re-Active Power Compensation Technique in Long Transmission System (75 Km) By Using Shunt Facts Control Device with Mat Lab Simlink Tool Dabberu.Venkateswara Rao, 1 Bodi.Srikanth 2 1, 2(Department

More information

Simple Near-field to Far-field Transformation Method Using Antenna Array-factor

Simple Near-field to Far-field Transformation Method Using Antenna Array-factor Journal of Wireless Networking and Communications 01, (4): 43-48 DOI: 10.593/j.jwnc.01004.03 Simple Near-field to Far-field Transformation Method Using Antenna Array-factor Hirokazu Kobayashi *, Yoshio

More information

Oscillators. An oscillator may be described as a source of alternating voltage. It is different than amplifier.

Oscillators. An oscillator may be described as a source of alternating voltage. It is different than amplifier. Oscillators An oscillator may be described as a source of alternating voltage. It is different than amplifier. An amplifier delivers an output signal whose waveform corresponds to the input signal but

More information

R10. III B.Tech. II Semester Supplementary Examinations, January POWER SYSTEM ANALYSIS (Electrical and Electronics Engineering) Time: 3 Hours

R10. III B.Tech. II Semester Supplementary Examinations, January POWER SYSTEM ANALYSIS (Electrical and Electronics Engineering) Time: 3 Hours Code No: R3 R1 Set No: 1 III B.Tech. II Semester Supplementary Examinations, January -14 POWER SYSTEM ANALYSIS (Electrical and Electronics Engineering) Time: 3 Hours Max Marks: 75 Answer any FIVE Questions

More information

Special-Purpose Operational Amplifier Circuits

Special-Purpose Operational Amplifier Circuits Special-Purpose Operational Amplifier Circuits Instrumentation Amplifier An instrumentation amplifier (IA) is a differential voltagegain device that amplifies the difference between the voltages existing

More information

Lecture 9: Smith Chart/ S-Parameters

Lecture 9: Smith Chart/ S-Parameters Lecture 9: Smith Chart/ S-Parameters Amin Arbabian Jan M. Rabaey EE142 Fall 2010 Sept. 23 rd, 2010 University of California, Berkeley Announcements HW3 was due at 3:40pm today You have up to tomorrow 3:30pm

More information

Identify and draw points, lines, line segments, rays, and angles. Recognize them in various contexts and familiar figures.

Identify and draw points, lines, line segments, rays, and angles. Recognize them in various contexts and familiar figures. Lesson 1 Homework 4 Name Date 1. Use the following directions to draw a figure in the box to the right. a. Draw two points: WW and XX. b. Use a straightedge to draw WWWW. c. Draw a new point that is not

More information

University of Portland EE 271 Electrical Circuits Laboratory. Experiment: Inductors

University of Portland EE 271 Electrical Circuits Laboratory. Experiment: Inductors University of Portland EE 271 Electrical Circuits Laboratory Experiment: Inductors I. Objective The objective of this experiment is to verify the relationship between voltage and current in an inductor,

More information

INSTANTANEOUS POWER CONTROL OF D-STATCOM FOR ENHANCEMENT OF THE STEADY-STATE PERFORMANCE

INSTANTANEOUS POWER CONTROL OF D-STATCOM FOR ENHANCEMENT OF THE STEADY-STATE PERFORMANCE INSTANTANEOUS POWER CONTROL OF D-STATCOM FOR ENHANCEMENT OF THE STEADY-STATE PERFORMANCE Ms. K. Kamaladevi 1, N. Mohan Murali Krishna 2 1 Asst. Professor, Department of EEE, 2 PG Scholar, Department of

More information

Electrical Engineering. Power Systems. Comprehensive Theory with Solved Examples and Practice Questions. Publications

Electrical Engineering. Power Systems. Comprehensive Theory with Solved Examples and Practice Questions. Publications Electrical Engineering Power Systems Comprehensive Theory with Solved Examples and Practice Questions Publications Publications MADE EASY Publications Corporate Office: 44-A/4, Kalu Sarai (Near Hauz Khas

More information

ECEN 615 Methods of Electric Power Systems Analysis Lecture 8: Advanced Power Flow

ECEN 615 Methods of Electric Power Systems Analysis Lecture 8: Advanced Power Flow ECEN 615 Methods of Electric Power Systems nalysis Lecture 8: dvanced Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering Texas &M University overbye@tamu.edu nnouncements Read Chapter

More information

6.014 Lecture 14: Microwave Communications and Radar

6.014 Lecture 14: Microwave Communications and Radar 6.014 Lecture 14: Microwave Communications and Radar A. Overview Microwave communications and radar systems have similar architectures. They typically process the signals before and after they are transmitted

More information

CDS 101/110: Lecture 8.2 PID Control

CDS 101/110: Lecture 8.2 PID Control CDS 11/11: Lecture 8.2 PID Control November 16, 216 Goals: Nyquist Example Introduce and review PID control. Show how to use loop shaping using PID to achieve a performance specification Discuss the use

More information

EC6503 Transmission Lines and WaveguidesV Semester Question Bank

EC6503 Transmission Lines and WaveguidesV Semester Question Bank UNIT I TRANSMISSION LINE THEORY A line of cascaded T sections & Transmission lines General Solution, Physicasignificance of the equations 1. Derive the two useful forms of equations for voltage and current

More information

Distance Protection of Cross-Bonded Transmission Cable-Systems

Distance Protection of Cross-Bonded Transmission Cable-Systems Downloaded from vbn.aau.dk on: April 19, 2019 Aalborg Universitet Distance Protection of Cross-Bonded Transmission Cable-Systems Bak, Claus Leth; F. Jensen, Christian Published in: Proceedings of the 12th

More information

Homework Assignment 09

Homework Assignment 09 Question 1 (2 points each unless noted otherwise) Homework Assignment 09 1. For SPICE, Explain very briefly the difference between the multiplier M and Meg, as in a resistor has value 2M versus a resistor

More information

Amateur Extra Manual Chapter 9.4 Transmission Lines

Amateur Extra Manual Chapter 9.4 Transmission Lines 9.4 TRANSMISSION LINES (page 9-31) WAVELENGTH IN A FEED LINE (page 9-31) VELOCITY OF PROPAGATION (page 9-32) Speed of Wave in a Transmission Line VF = Velocity Factor = Speed of Light in a Vacuum Question

More information

Interline Power Flow Controller: Review Paper

Interline Power Flow Controller: Review Paper Vol. (0) No. 3, pp. 550-554 ISSN 078-365 Interline Power Flow Controller: Review Paper Akhilesh A. Nimje, Chinmoy Kumar Panigrahi, Ajaya Kumar Mohanty Abstract The Interline Power Flow Controller (IPFC)

More information

Physical Structure of CMOS Integrated Circuits

Physical Structure of CMOS Integrated Circuits Physical Structure of CMOS Integrated Circuits Dae Hyun Kim EECS Washington State University References John P. Uyemura, Introduction to VLSI Circuits and Systems, 2002. Chapter 3 Neil H. Weste and David

More information

Kerwin, W.J. Passive Signal Processing The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

Kerwin, W.J. Passive Signal Processing The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000 Kerwin, W.J. Passive Signal Processing The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 000 4 Passive Signal Processing William J. Kerwin University of Arizona 4. Introduction

More information

EC TRANSMISSION LINES AND WAVEGUIDES TRANSMISSION LINES AND WAVEGUIDES

EC TRANSMISSION LINES AND WAVEGUIDES TRANSMISSION LINES AND WAVEGUIDES TRANSMISSION LINES AND WAVEGUIDES UNIT I - TRANSMISSION LINE THEORY 1. Define Characteristic Impedance [M/J 2006, N/D 2006] Characteristic impedance is defined as the impedance of a transmission line measured

More information

55:141 Advanced Circuit Techniques Switching Regulators

55:141 Advanced Circuit Techniques Switching Regulators 55:141 Advanced Circuit Techniques Switching Regulators Material: ecture Notes, Handouts, and Sections of Chapter 11 of Franco A. Kruger 55:141: Advanced Circuit Techniques The University of Iowa Switching

More information

Performance Analysis of DFIG based Wind Energy Conversion System Using Direct Power Controller

Performance Analysis of DFIG based Wind Energy Conversion System Using Direct Power Controller Performance Analysis of DFIG based Wind Energy Conversion System Using Direct Power Controller V. Kaarthikeyan 1, G. Madusudanan 2 1 Student, Valliammai Engineering College, Chennai, Tamil Nadu, India

More information

Eureka Math. Grade 4, Module 4. Student File_A. Contains copy-ready classwork and homework as well as templates (including cut outs)

Eureka Math. Grade 4, Module 4. Student File_A. Contains copy-ready classwork and homework as well as templates (including cut outs) A Story of Units Eureka Math Grade 4, Module 4 Student File_A Contains copy-ready classwork and homework as well as templates (including cut outs) Published by the non-profit Great Minds. Copyright 2015

More information

Unit WorkBook 4 Level 4 ENG U19 Electrical and Electronic Principles LO4 Digital & Analogue Electronics 2018 Unicourse Ltd. All Rights Reserved.

Unit WorkBook 4 Level 4 ENG U19 Electrical and Electronic Principles LO4 Digital & Analogue Electronics 2018 Unicourse Ltd. All Rights Reserved. Pearson BTEC Levels 4 Higher Nationals in Engineering (RQF) Unit 19: Electrical and Electronic Principles Unit Workbook 4 in a series of 4 for this unit Learning Outcome 4 Digital & Analogue Electronics

More information

ELEC273 Lecture Notes Set 4, Mesh Analysis

ELEC273 Lecture Notes Set 4, Mesh Analysis ELEC273 Lecture Notes Set 4, Mesh Analysis The course web site is: http://users.encs.concordia.ca/~trueman/web_page_273.htm The list of homework problems is in the course outline. For this week: Do these

More information